On recursive trees with a unique infinite branch

Abstract

In this paper we analyze the Turing degree of an infinite branch in a recursive tree T ⊆ ω > ω T \subseteq {\omega ^{ > \omega }} and its relation to the well-founded part of the tree. It is, of course, not surprising that the two notions are related, but it is of a certain technical interest (in terms of the coding procedure used) to establish the exact interrelation. An interpretation of our result in terms of a Cantor-Bendixson derivative operation on trees T ⊆ ω > ω T \subseteq {\omega ^{ > \omega }} is given.